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Fully-Diverse Lattices from Ramified Cyclic Extensions of Prime Degree
(2020-01-01)
Let p be an odd prime. Algebraic lattices of full diversity in dimension p are obtained from ramified cyclic extensions of degree p. The 3, 5, and 7-dimensional lattices are optimal with respect to sphere packing density ...
Constructions of algebraic lattices
(Sociedade Brasileira de Matemática Aplicada e Computacional, 2010-01-01)
In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These ...
Algebraic constructions of densest lattices
(Elsevier B.V., 2015-05-01)
The aim of this paper is to investigate rotated versions of the densest known lattices in dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free Z-modules that are not ideals in subfields of cyclotomic ...
Frontal operators in distributive lattices with a generalized implication
(WorldScientific Open Access, 2015-09)
We introduce a family of extensions of bounded distributive lattices. These extensions are obtained by adding two operations: an internal unary operation, and a function (called generalized implication) that maps pair of ...
Reticulados algébricos via corpos abelianos
(Universidade Estadual Paulista (Unesp), 2008-02-22)
Dado um ideal A do anel dos inteiros algébricos de um corpo de números, tem-se que a imagem deste ideal via o homomorfissmo de Minkowski é um reticulado no Rn, chamado de reticulado algébrico. Deste modo, o principal ...
Reticulados algébricos via corpos abelianos
(Universidade Estadual Paulista (Unesp), 2008-02-22)
Dado um ideal A do anel dos inteiros algébricos de um corpo de números, tem-se que a imagem deste ideal via o homomorfissmo de Minkowski é um reticulado no Rn, chamado de reticulado algébrico. Deste modo, o principal ...
Kleene algebras with implication
(Springer, 2017-07)
Inspired by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras, in this paper we study an equivalence for certain categories whose objects are algebras with implication ...
Collapse of K - Rb Fermi-Bose mixtures in optical lattices
(World Scientific, 2006-12)
We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain ...